Question

In two digit number the units digit exceeds its tenth digit by 2. The product of the given number and the sum of digit is 144. Find the numbers

Answer 1

ANSWER : .........

Let the units digit be X

And tens digits be Y

Number=10Y+X

Units digit exceeds tens digit by 2

Hence X−Y=2 

X=2+Y⟹(i)

And (10Y+X)(X+Y)=144

10XY+10Y2+X2+XY=144

11XY+10Y2+X2=144⟹(ii)

Substitute X from (i) in (ii) and get

11(2+Y)Y+10Y2+(2+Y)2=144

22Y+11Y2+10Y2+4+4Y+Y2=144

22X+11X2+40+40X+10X2=144

22Y2+26Y−140=0

11Y2+13Y−70=0

11Y2+35Y−22Y−70=0

Y(11Y+35)−2(11Y+35)=0

(y−2)(11Y+35)=0

Now either (Y−2)=0 

Y=2

Or 11Y+35=0 

Y=11−35

Since Y is non negative

Hence Y=2 and X=2+Y=2+2=4

Hence required number =4

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